GATE 2025 EE – Question 32
Consider a distribution feeder, with $R/X$ ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is __________ (round off to three decimal places).
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Correct answer: 0.97 to 0.99
Explanation
For a load current $I$ at angle $\varphi$ (lagging), the approximate voltage drop is $\Delta V\approx I\,(R\cos\varphi+X\sin\varphi)$. For a fixed $|I|$ this is maximum when $\tan\varphi=X/R=1/5$, i.e. $\varphi=\tan^{-1}0.2=11.31^\circ$. The power factor is $\cos11.31^\circ=0.981$ (lagging).